CHICAGO -- Ryan Dempster tied the Cubs' record with a 33-inning scoreless streak, pitching six solid frames and leading Chicago over the Arizona Diamondbacks 4-1 on Saturday.

Dempster matched the club shutout streak set by Ken Holtzman in 1969.

Dempster (5-3) allowed four hits and set a career best by winning his fifth straight start. He leads the majors with a 1.86 ERA.

Cubs manager Dale Sveum limited Dempster to 89 pitches. The right-hander made his second start since coming off the disabled list with tightness in his pitching shoulder.

Dempster struck out five and walked three. With the Cubs far back in the playoff race and Dempster in the last season of a four-year contract, he has become a possible trade option for contending teams.

Darwin Barney hit an RBI double for the Cubs, who have won 11 of their last 15 games.

Chris Young homered for Arizona in the seventh off James Russell. The Diamondbacks have lost eight of 11.

Cubs closer Carlos Marmol pitched a scoreless ninth for his ninth save in 11 chances. Marmol allowed a leadoff double to Stephen Drew and walked Young. Geoff Blum followed with a deep fly ball to right, but Reed Johnson made a nice running catch up against the ivy, then Marmol got pinch hitter Jason Kubel to hit into a double play to end the game.

Joe Saunders (4-6) returned after being on the disabled list with a left shoulder strain and pitched six innings. He allowed three earned runs and eight hits.

Luis Valbuena led off the Cubs third with a single and Dempster sacrificed. Johnson reached on a bunt single and Starlin Castro beat out a potential inning-ending double play as Valbuena scored.

In the fourth, Alfonso Soriano led off with a single and later scored on Barney's two-out double. Three pitches later, Valbuena singled up the middle for a 3-0 lead.

The Cubs scored in the sixth on an error and Barney's double-play ball.

NOTES: The Diamondbacks optioned LHP Patrick Corbin to Triple-A Reno to make room on the roster for Saunders. Diamondbacks manager Kirk Gibson said Corbin will work as a starter at Reno. He started five games for Arizona this year but had been appearing out of the bullpen of late. ... Kubel (right hamstring tightness) was held out of the starting lineup. Gibson said Kubel was still sore. Kubel was removed in the seventh inning of Friday's 8-1 loss after slipping several times on the slick field.